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Nonlinear Differential Equations in Abstract Spaces

1981 Mathematics
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Release : 1981
Genre : Mathematics
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Nonlinear Differential Equations in Abstract Spaces by : V. Lakshmikantham

Download or read book Nonlinear Differential Equations in Abstract Spaces written by V. Lakshmikantham. This book was released on 1981. Available in PDF, EPUB and Kindle. Book excerpt: Many problems in partial differential equations which arise from physical models can be considered as ordinary differential equations in appropriate infinite dimensional spaces, for which elegant theories and powerful techniques have recently been developed. This book gives a detailed account of the current state of the theory of nonlinear differential equations in a Banach space, and discusses existence theory for differential equations with continuous and discontinuous right-hand sides. Of special importance is the first systematic presentation of the very important and complex theory of multivalued discontinuous differential equations

Nonlinear Equations in Abstract Spaces

2014-05-27 Mathematics
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Release : 2014-05-27
Genre : Mathematics
Kind : eBook
Book Rating : 109/5 ( reviews)

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Book Synopsis Nonlinear Equations in Abstract Spaces by : V. Lakshmikantham

Download or read book Nonlinear Equations in Abstract Spaces written by V. Lakshmikantham. This book was released on 2014-05-27. Available in PDF, EPUB and Kindle. Book excerpt: Many problems in partial differential equations which arise from physical models can be considered as ordinary differential equations in appropriate infinite dimensional spaces, for which elegant theories and powerful techniques have recently been developed. This book gives a detailed account of the current state of the theory of nonlinear differential equations in a Banach space, and discusses existence theory for differential equations with continuous and discontinuous right-hand sides. Of special importance is the first systematic presentation of the very important and complex theory of multivalued discontinuous differential equations.

Nonlinear Integral Equations in Abstract Spaces

2013-11-22 Mathematics
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Release : 2013-11-22
Genre : Mathematics
Kind : eBook
Book Rating : 817/5 ( reviews)

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Book Synopsis Nonlinear Integral Equations in Abstract Spaces by : Dajun Guo

Download or read book Nonlinear Integral Equations in Abstract Spaces written by Dajun Guo. This book was released on 2013-11-22. Available in PDF, EPUB and Kindle. Book excerpt: Many problems arising in the physical sciences, engineering, biology and ap plied mathematics lead to mathematical models described by nonlinear integral equations in abstract spaces. The theory of nonlinear integral equations in ab stract spaces is a fast growing field with important applications to a number of areas of analysis as well as other branches of science. This book is devoted to a comprehensive treatment of nonlinear integral equations in abstract spaces. It is the first book that is dedicated to a systematic development of this subject, and it includes the developments during recent years. Chapter 1 introduces some basic results in analysis, which will be used in later chapters. Chapter 2, which is a main portion of this book, deals with nonlin ear integral equations in Banach spaces, including equations of Fredholm type, of Volterra type and equations of Hammerstein type. Some applica equations tions to nonlinear differential equations in Banach spaces are given. We also discuss an integral equation modelling infectious disease as a typical applica tion. In Chapter 3, we investigate the first order and second order nonlinear integro-differential equations in Banach spaces including equations of Volterra type and equations of mixed type. Chapter 4 is devoted to nonlinear impulsive integral equations in Banach spaces and their applications to nonlinear impul sive differential equations in Banach spaces.

Differential Equations in Abstract Spaces

1972-06-16 Computers
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Release : 1972-06-16
Genre : Computers
Kind : eBook
Book Rating : 940/5 ( reviews)

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Book Synopsis Differential Equations in Abstract Spaces by : Lakshmikantham

Download or read book Differential Equations in Abstract Spaces written by Lakshmikantham. This book was released on 1972-06-16. Available in PDF, EPUB and Kindle. Book excerpt: Differential Equations in Abstract Spaces

Nonlinear Differential Equations in Ordered Spaces

2000-06-14 Mathematics
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Release : 2000-06-14
Genre : Mathematics
Kind : eBook
Book Rating : 684/5 ( reviews)

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Book Synopsis Nonlinear Differential Equations in Ordered Spaces by : S. Carl

Download or read book Nonlinear Differential Equations in Ordered Spaces written by S. Carl. This book was released on 2000-06-14. Available in PDF, EPUB and Kindle. Book excerpt: Extremality results proved in this Monograph for an abstract operator equation provide the theoretical framework for developing new methods that allow the treatment of a variety of discontinuous initial and boundary value problems for both ordinary and partial differential equations, in explicit and implicit forms. By means of these extremality results, the authors prove the existence of extremal solutions between appropriate upper and lower solutions of first and second order discontinuous implicit and explicit ordinary and functional differential equations. They then study the dependence of these extremal solutions on the data. The authors begin by developing an existence theory for an abstract operator equation in ordered spaces and offer new tools for dealing with different kinds of discontinuous implicit and explicit differential equation problems. They present a unified approach to the existence of extremal solutions of quasilinear elliptic and parabolic problems and extend the upper and lower solution method to elliptic and parabolic inclusion of hemivariation type using variational and nonvariational methods. Nonlinear Differential Equations in Ordered Spaces includes research that appears for the first time in book form and is designed as a source book for pure and applied mathematicians. Its self-contained presentation along with numerous worked examples and complete, detailed proofs also make it accessible to researchers in engineering as well as advanced students in these fields.

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